I just have finished installing Anchor, and here I leave some solutions to he couple issues I had faced and are not in the documentation.
First of all, if at the install fase you get an SQL error, SQLSTATE[28000] [1045] Access denied for user 'root'@'localhost' (using password: YES), you just need to create the user and database yourself. You can access to the mysql command line and run:

CREATE USER anchor_user@localhost IDENTIFIED BY 'password';   
GRANT ALL ON anchor.* TO anchor_user;   

Then you can see if the user has the right access running: SHOW GRANTS FOR anchor_user

The other problem I ran into was related to the nginX configuration recommended in the documentation. The problem was because I have the blog in a subfolder, and the solution is simple. Just change (or add):

    location /blog {   
        try_files $uri $uri/ /index.php;